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A Fermion Doublet With Chiral Gauge Interaction On A Lattice: We present a new staggered discretization of the Dirac operator. Doubling
gives only a doublet of Dirac fermions which we propose to interpret as a
physical (lepton or quark) doublet. If coupled with gauge fields, an
$(1+\gamma^5)$ chiral interaction appears in a natural way. We define a
generalization for curved background which does not require tetrad variables.
The approach suggests a natural explanation for the three fermion families. | hep-lat |
Strong-coupling effective action(s) for SU(3) Yang-Mills: We apply strong-coupling expansion techniques to finite-temperature lattice
pure gauge theory, obtaining dimensionally reduced $Z_N$-symmetric effective
theories. The analytic mappings between the effective couplings and the
original one, viz. $\beta$, allow to estimate the transition point $\beta_c$ of
the 4D theory for a large range of the imaginary-time extent $N_\tau$ of the
lattice. We study the models for SU(3) via Monte Carlo simulation, finding
satisfactory agreement with the critical point of the original theories
especially at low $N_\tau$. We have fixed an error in the group measure used in
arXiv:1010.0951 and provide here the correct numerical results. | hep-lat |
Topological susceptibility in two-flavor QCD: We compute the topological susceptibility in QCD with two flavors of
dynamical fermions using numerical simulation with overlap fermions. | hep-lat |
Hadron Spectrum with Wilson fermions: We present results of a high statistics study of the quenched spectrum using
Wilson fermions at $\beta=6.0$ on $32^3 \times 64$ lattices. We calculate the
masses of mesons and baryons composed of both degenerate and non-degenerate
quarks. Using non-degenerate quark combinations allows us to study baryon mass
splittings in detail. We find significant deviations from the lowest order
chiral expansion, deviations that are consistent with the expectations of
quenched chiral perturbation theory. We find that there is a $\sim 20%$
systematic error in the extracted value of $m_s$, depending on the meson mass
ratio used to set its value. Using the largest estimate of $m_s$ we find that
the extrapolated octet mass-splittings are in agreement with the experimental
values, as is $M_\Delta - M_N$, while the decuplet splittings are 30% smaller
than experiment. Combining our results with data from the GF11 collaboration we
find considerable ambiguity in the extrapolation to the continuum limit. Our
preferred values are $M_N / M_\rho = 1.38(7)$ and $M_\Delta / M_\rho =
1.73(10)$, suggesting that the quenched approximation is good to only $\sim
10-15%$. We also analyze the $O(ma)$ discretization errors in heavy quark
masses. | hep-lat |
Progress applying density of states for gravitational waves: Many models of composite dark matter feature a first-order confinement
transition in the early Universe, which would produce a stochastic background
of gravitational waves that will be searched for by future gravitational-wave
observatories. We present work in progress using lattice field theory to
predict the properties of such first-order transitions. Targeting SU(N)
Yang--Mills theories, this work employs the Logarithmic Linear Relaxation (LLR)
density of states algorithm to avoid super-critical slowing down at the
transition. | hep-lat |
$I=0$ $ππ$ $s$-wave scattering length from lattice QCD: We deliver lattice results for the $I=0$ $\pi\pi$ elastic $s$-wave scattering
length calculated with the MILC $N_f=3$ flavors of the Asqtad-improved
staggered fermions. The scattering phase shifts are determined by L\"uscher's
formula from the energy-eigenvalues of $\pi\pi$ systems at one center of mass
frame and four moving frames using the moving wall source technique. Our
measurements are good enough to resolve the scattering length $a$ and effective
range $r$, moreover, it allows us to roughly estimate the shape parameter $P$.
Using our lattice results, the scattering length $a$ and effective range $r$ at
the physical point are extrapolated by chiral perturbation theory. Our results
are reasonably consistent with the Roy equation determinations and the newer
experimental data. Numerical computations are carried out with two MILC fine
($a\approx0.09$~fm, $L^3 \times T = 40^3\times 96$) and one MILC superfine
($a\approx0.06$~fm, $L^3 \times T = 48^3\times 144$) lattice ensembles at three
pion masses of $m_\pi\sim247~{\rm MeV}$, $249~{\rm MeV}$, and $314~{\rm MeV}$,
respectively. | hep-lat |
On meson spectral functions at high temperature and nonzero momentum: In the high-temperature phase of QCD meson spectral functions at nonzero
momentum are expected to have a nontrivial and interesting structure. In order
to provide a reference point for lattice studies employing e.g. the Maximal
Entropy Method, we discuss several characteristics of meson spectral functions
in the infinite-temperature limit. We report on ongoing work in quenched QCD
with staggered fermions. | hep-lat |
Vacuum Entanglement Harvesting in the Ising Model: The low-energy states of quantum many body systems, such as spin chains, are
entangled. Using tensor network computations, we demonstrate a protocol that
distills Bell pairs out of the ground state of the prototypical
transverse-field Ising model. We explore the behavior of rate of entanglement
distillation in various phases, and possible optimizations of the protocol.
Finally, we comment on the protocol as we approach quantum criticality defining
a continuum field theory. | hep-lat |
Magnetic and electric screening masses from Polyakov-loop correlations: Screening properties of the quark gluon plasma are studied from Polyakov-loop
correlation in lattice QCD simulations with two flavors of improved Wilson
quarks at temperatures $T/\Tpc \simeq 1$--4 where $\Tpc$ is the pseudocritical
temperature. Using the Euclidean-time reflection symmetry and the charge
conjugation symmetry, we introduce various types of Polyakov-loop correlation
functions and extract screening masses in magnetic and electric sectors. We
find that the temperature dependence of the screening masses are well described
by the weak coupling expansion. We also find that a ratio of the screening
masses in the electric sector to the magnetic sector shows qualitative
agreement with a prediction from the dimensionally-reduced effective field
theory and the N=4 supersymmetric Yang-Mills theory at $1.3 < T/\Tpc < 3$. | hep-lat |
The quark-mass dependence of the potential energy between static colour
sources in the QCD vacuum with light and strange quarks: The low-lying energy spectrum of the static-colour-source-anti-source system
in a vacuum containing light and strange quarks is computed using lattice QCD
for a range of different light quark masses. The resulting levels are described
using a simple model Hamiltonian and the parameters in this model are
extrapolated to the physical light-quark masses. In this framework, the QCD
string tension is found to be $\sqrt{\sigma}=445(3)_{\rm stat}(6)_{\rm sys}$
MeV. | hep-lat |
Determinant Calculations Using Random Walk Worldline Loops: We use statistical ensembles of worldline loops generated by random walk on
hypercubic lattices to calculate matter determinants in background Yang-Mills
fields. | hep-lat |
Scaling test of quenched Wilson twisted mass QCD at maximal twist: We present the results of an extended scaling test of quenched Wilson twisted
mass QCD. We fix the twist angle by using two definitions of the critical mass,
the first obtained by requiring the vanishing of the pseudoscalar meson mass
m_PS for standard Wilson fermions and the second by requiring restoration of
parity at non-zero value of the twisted mass mu and subsequently extrapolating
to mu=0. Depending on the choice of the critical mass we simulate at values of
beta in [5.7,6.45], for a range of pseudoscalar meson masses 250 MeV < m_PS < 1
GeV and we perform the continuum limit for the pseudoscalar meson decay
constant f_PS and various hadron masses (vector meson m_V, baryon octet m_oct
and baryon decuplet m_dec) at fixed value of r_0 m_PS. For both definitions of
the critical mass, lattice artifacts are consistent with O(a) improvement.
However, with the second definition, large O(a^2) discretization errors present
at small quark mass with the first definition are strongly suppressed. The
results in the continuum limit are in very good agreement with those from the
Alpha and CP-PACS Collaborations. | hep-lat |
Capillary Waves in Binder's Approach to the Interface Tension: In Binder's approach the reduced interface tension sigma of the Ising model
in the broken phase is determined from the finite volume effects of the
partition function Z(M) at fixed total magnetization M. For small |M| the
partition function of a system of size L^d with periodic boundary conditions is
dominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma
L^{d-1}). Capillary wave fluctuations of the interfaces correct this result to
Z(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential
behavior allows an improved fit of numerical data, and a determination of the
interface stiffness. | hep-lat |
Development of Lattice QCD Tool Kit on Cell Broadband Engine Processor: We report an implementation of a code for SU(3) matrix multiplication on
Cell/B.E., which is a part of our project, Lattice Tool Kit on Cell/B.E.. On
QS20, the speed of the matrix multiplication on SPE in single precision is
227GFLOPS and it becomes 20GFLOPS {this vaule was remeasured and corrcted.}
together with data transfer from main memory by DNA transfer, which is 4.6% of
the hardware peak speed (460GFLOPS), and is 7.4% of the theoretical peak speed
of this calculation (268.77GFLOPS). We briefly describe our tuning procedure. | hep-lat |
Tensor renormalization group approach to (1+1)-dimensional SU(2)
principal chiral model at finite density: We apply the tensor renormalization group method to the (1+1)-dimensional
SU(2) principal chiral model at finite chemical potential with the use of the
Gauss-Legendre quadrature to discretize the SU(2) Lie group. The internal
energy at vanishing chemical potential $\mu=0$ shows good consistency with the
prediction of the strong and weak coupling expansions. This indicates an
effectiveness of the Gauss-Legendre quadrature for the partitioning of the
SU(2) Lie group. In the finite density region with $\mu\ne 0$ at the strong
coupling we observe the Silver-Blaze phenomenon for the number density. | hep-lat |
Color superconductivity in a small box: a complex Langevin study: It is expected that the color superconductivity (CSC) phase appears in QCD at
low temperature and high density. On the basis of the lattice perturbation
theory, a possible parameter region in which the CSC occurs has been predicted.
In this work, we perform complex Langevin simulation on an $8^3\times 128$
lattice using four-flavor staggered fermions. We find, in particular, that the
quark number has plateaux with respect to the chemical potential similar to our
previous study, indicating the formation of the Fermi sphere. A
diquark-antidiquark operator, which is an order parameter of color
superconductivity, is formulated on the lattice using the U(1) noise. Our
result for this operator is found to fluctuate violently when the Fermi surface
coincides with the energy levels of quarks. We also discuss partial restoration
of the chiral symmetry at high density. | hep-lat |
Surface operator study in SU(2) gauge field theory: The surface operator in an SU(2) gauge field theory is studied. We analyze
Abelian projection of the SU(2) symmetry to the U(1) group calculating the
surface parameter. The surface parameter dependence on the surface area and
volume is studied in confinement and deconfinement phases. It is shown the
spatial and temporal surface operators exhibit nontrivial area dependence in
the confinement and deconfinement phases. It is shown also that there is no
volume law for the operators defined on a cubic surface. | hep-lat |
Non-Perturbative Renormalization of Lattice Four-Fermion Operators
without Power Subtractions: A general non-perturbative analysis of the renormalization properties of
$\Delta I=3/2$ four-fermion operators in the framework of lattice
regularization with Wilson fermions is presented. We discuss the
non-perturbative determination of the operator renormalization constants in the
lattice Regularization Independent (RI or MOM) scheme. We also discuss the
determination of the finite lattice subtraction coefficients from Ward
Identities. We prove that, at large external virtualities, the determination of
the lattice mixing coefficients, obtained using the RI renormalization scheme,
is equivalent to that based on Ward Identities, in the continuum and chiral
limits. As a feasibility study of our method, we compute the mixing matrix at
several renormalization scales, for three values of the lattice coupling
$\beta$, using the Wilson and tree-level improved SW-Clover actions. | hep-lat |
Probing hadron wave functions in Lattice QCD: Gauge-invariant equal-time correlation functions are calculated in lattice
QCD within the quenched approximation and with two dynamical quark species.
These correlators provide information on the shape and multipole moments of the
pion, the rho, the nucleon and the $\Delta$. | hep-lat |
The Anderson transition in QCD with $N_f=2+1+1$ twisted mass quarks:
overlap analysis: Chiral Random Matrix Theory has proven to describe the spectral properties of
low temperature QCD very well. However, at temperatures above the chiral
symmetry restoring transition it can not provide a global description. The
level-spacing distribution in the lower part of the spectrum of the Dirac
operator is Poisson-like. There the eigenmodes are localized in space-time and
separated from the rest of the spectrum by a so-called mobility edge. In
analogy to Anderson localization in condensed-matter systems with random
disorder this has been called the QCD-Anderson transition. Here, we study the
localization features of the low-lying eigenmodes of the massless overlap
operator on configurations generated with $N_f=2+1+1$ twisted mass Wilson sea
quarks and present results concerning the temperature dependence of the
mobility edge and the mechanism of the quark-mode localization. We have used
various methods to fix the spectral position of the delocalization transition
and verify that the mobility edge extrapolates to zero at a temperature within
the chiral transition region. | hep-lat |
Determining the chiral condensate from the distribution of the winding
number beyond topological susceptibility: The first two non-trivial moments of the distribution of the topological
charge (or gluonic winding number), i.e., the topological susceptibility and
the fourth cumulant, can be computed in lattice QCD simulations and exploited
to constrain the pattern of chiral symmetry breaking. We compute these two
topological observables at next-to-leading order in three-flavour Chiral
Perturbation Theory, and we discuss the role played by the eta propagation in
these expressions. For hierarchies of light-quark masses close to the physical
situation, we show that the fourth cumulant has a much better sensitivity than
the topological susceptibility to the three-flavour quark condensate, and thus
constitutes a relevant tool to determine the pattern of chiral symmetry
breaking in the limit of three massless flavours. We provide the complete
formulae for the two topological observables in the isospin limit, and predict
their values in the particular setting of the recent analysis of the RBC/UKQCD
collaboration. We show that a combination of the topological susceptibility and
the fourth cumulant is able to pin down the three-flavour condensate in a
particularly clean way in the case of three degenerate quarks. | hep-lat |
Semileptonic decays $B\rightarrow D^{(*)}lν$ at nonzero recoil: We have analyzed the semileptonic decays $B\rightarrow D\ell\nu$ and
$B\rightarrow D^*\ell\nu$ on the full suite of MILC (2+1)-flavor asqtad
ensembles with lattice spacings as small as 0.045 fm and light-to-strange-quark
mass ratios as low as 1/20. We use the Fermilab interpretation of the clover
action for heavy valence quarks and the asqtad action for light valence quarks.
We compute the hadronic form factors for $B\rightarrow D$ at both zero and
nonzero recoil and for $B\rightarrow D^*$ at zero recoil. We report our results
for $|V_{cb}|$. | hep-lat |
Beauty mesons in $N_f=2+1+1+1 $ lattice QCD with exact chiral symmetry: We present the first study of $N_f=2+1+1+1$ lattice QCD with domain-wall
quarks. The $(b, c, s)$ quarks are physical, while the $(u, d)$ quarks are
heavier than their physical masses, with the pion mass $ \sim 700 $ MeV. The
gauge ensemble is generated by hybrid Monte Carlo simulation with the Wilson
gauge action for the gluons, and the optimal domain-wall fermion action for the
quarks. Using point-to-point quark propagators, we measure the time-correlation
functions of quark-antiquark meson interpolators with quark contents $\bar b
b$, $\bar b c$, $\bar b s$, and $ \bar c c$, and obtain the masses of the
low-lying mesons. They are in good agreement with the experimental values, plus
some predictions which have not been observed in experiments. Moreover, we also
determine the masses of $(b, c, s)$ quarks. | hep-lat |
Improved Lattice Renormalization Group Techniques: We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge
theory with $N_f = 12$ massless fundamental fermions, using the
non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group
two-lattice matching technique. We use a short Wilson flow to approach the
renormalized trajectory before beginning RG blocking steps. By optimizing the
length of the Wilson flow, we are able to determine an $s_b$ corresponding to a
unique discrete $\beta$ function, after a few blocking steps. We carry out this
study using new ensembles of 12-flavor gauge configurations generated with
exactly massless fermions, using volumes up to $32^4$. The results are
consistent with the existence of an infrared fixed point (IRFP) for all
investigated lattice volumes and number of blocking steps. We also compare
different renormalization schemes, each of which indicates an IRFP at a
slightly different value of the bare coupling, as expected for an IR-conformal
theory. | hep-lat |
Instanton Distribution in Quenched and Full QCD: In order to optimize cooling as a technique to study the instanton content of
the QCD vacuum, we have studied the effects of alternative algorithms, improved
actions and boundary conditions on the evolution of single instantons and
instanton anti-instanton pairs. Using these results, we have extracted and
compared the instanton content of quenched and full QCD. | hep-lat |
Compactified N=1 supersymmetric Yang-Mills theory on the lattice:
Continuity and the disappearance of the deconfinement transition: Fermion boundary conditions play a relevant role in revealing the confinement
mechanism of N=1 supersymmetric Yang-Mills theory with one compactified
space-time dimension. A deconfinement phase transition occurs for a
sufficiently small compactification radius, equivalent to a high temperature in
the thermal theory where antiperiodic fermion boundary conditions are applied.
Periodic fermion boundary conditions, on the other hand, are related to the
Witten index and confinement is expected to persist independently of the length
of the compactified dimension. We study this aspect with lattice Monte Carlo
simulations for different values of the fermion mass parameter that breaks
supersymmetry softly. We find a deconfined region that shrinks when the fermion
mass is lowered. Deconfinement takes place between two confined regions at
large and small compactification radii, that would correspond to low and high
temperatures in the thermal theory. At the smallest fermion masses we find no
indication of a deconfinement transition. These results are a first signal for
the predicted continuity in the compactification of supersymmetric Yang-Mills
theory. | hep-lat |
The static quark self-energy at large orders from NSPT: Using Numerical Stochastic Perturbation Theory (NSPT), we calculate the
static self-energy of SU(3) gauge theory up to order \alpha^{20}. Simulations
on a large set of different lattice volumes allow for a careful treatment of
finite size effects. The resulting infinite volume perturbative series of the
static self-energy is in remarkable agreement with the predicted asymptotic
behaviour of high order expansions, namely with a factorial growth of
perturbative coefficients known as renormalon. | hep-lat |
Form and index of Ginsparg-Wilson fermions: We clarify the questions rised by a recent example of a lattice Dirac
operator found by Chiu. We show that this operator belongs to a class based on
the Cayley transformation and that this class on the finite lattice generally
does not admit a nonvanishing index, while in the continuum limit, due to
operator properties in Hilbert space, this defect is no longer there. Analogous
observations are made for the chiral anomaly. We also elaborate on various
aspects of the underlying sum rule for the index. | hep-lat |
A library of extended high-temperature expansions of basic observables
for the spin S Ising models on two- and three-dimensional lattices: We present an on-line library of unprecedented extension for high-temperature
expansions of basic observables in the Ising models of general spin S, with
nearest-neighbor interactions.
We have tabulated through order beta^{25} the series for the nearest-neighbor
correlation function, the susceptibility and the second correlation moment in
two dimensions on the square lattice, and, in three dimensions, on the
simple-cubic and the body-centered cubic lattices. The expansion of the second
field derivative of the susceptibility is also tabulated through beta^{23} for
the same lattices. We have thus added several terms (from four up to thirteen)
to the series already published for spin
S=1/2,1,3/2,2,5/2,3,7/2,4,5,infinity. | hep-lat |
Gribov copies, Lattice QCD and the gluon propagator: We address the problem of Gribov copies in lattice QCD. The gluon propagator
is computed, in the Landau gauge, using 302 ($\beta = 5.8$) $12^4$
configurations gauge fixed to different copies. The results of the simulation
shows that: i) the effect of Gribov copies is small (less than 10%); ii) Gribov
copies change essentially the lowest momenta components ($q < 2.6$ GeV); iii)
within the statistical accuracy of our simulation, the effect of Gribov copies
is resolved if statistical errors are multiplied by a factor of two or three.
Moreover, when modelling the gluon propagator, different sets of Gribov copies
produce different sets of parameters not, necessarily, compatible within one
standard deviation. Finally, our data supports a gluon propagator which, for
large momenta, behaves like a massive gluon propagator with a mass of 1.1 GeV. | hep-lat |
Quenched scalar meson correlator with Domain Wall Fermions: We study the singlet and non-singlet scalar-meson masses using domain wall
fermions and the quenched approximation. The singlet mass is found to be
smaller than the non-singlet mass and indicates that the lowest singlet meson
state could be lighter than 1 GeV. The two-point functions for very small quark
masses are compared with expectations from the small-volume chiral perturbation
theory and the presence of fermionic zero modes. | hep-lat |
The sign problem and the Lefschetz thimble: Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with
the sign problem that hinders Monte Carlo simulations of many quantum field
theories (QFTs). The approach consists in formulating the QFT on a Lefschetz
thimble. In this paper we concentrate on the application to a scalar field
theory with a sign problem. In particular, we review the formulation and the
justification of the approach, and we also describe the Aurora Monte Carlo
algorithm that we are currently testing. | hep-lat |
Finite Temperature Phase Transition in SU(2) Lattice Gauge Theory with
Extended Action: We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge
theory at finite temperature by Monte Carlo simulations. We find that the
finite temperature deconfinement phase transition line joins the first order
bulk phase transition line at its endpoint. Moreover, across the bulk
transition line, the Polyakov loop undergoes a discontinuous jump implying the
existence of both confining and deconfining phases on its two sides.
Implications for universality and the nature of the confining-deconfining
transition are discussed. | hep-lat |
Investigation of Doubly Heavy Tetraquark Systems using Lattice QCD: We search for possibly existent bound states in the heavy-light tetraquark
channels with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $
\bar{b}\bar{c}ud $ using lattice QCD. We carry out calculations on several
gauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and
consider a basis of local and non-local interpolators. Besides extracting the
energy spectrum from the correlation matrices, we also perform a L\"uscher
analysis to extrapolate our results to infinite volume. | hep-lat |
Width of the flux tube in compact U(1) gauge theory in three dimensions: We study the squared width and the profile of flux tubes in compact U(1)
lattice gauge theory in three spacetime dimensions. The results obtained from
numerical calculations in the dual formulation of this confining theory are
compared with predictions from an effective bosonic-string model and from the
dual-superconductor model: it is found that the former fails at describing the
quantitative features of the flux tube, while the latter is in good agreement
with Monte Carlo data. The analytical interpretation of these results (in the
light of the semi-classical analysis by Polyakov) is pointed out, and a
comparison with non-Abelian gauge theories in four spacetime dimensions is
discussed. | hep-lat |
Ising description of the transition region in SU(3) gauge theory at
finite temperature: We attempt the numerical construction of an effective action in three
dimensions for Ising spins which represent the Wilson lines in the
four-dimensional SU(3) gauge theory at finite temperature. For each
configuration of the gauge theory, each spin is determined by averaging the
Wilson lines over a small neighborhood and then projecting the average to +/-1
according to whether the neighborhood is ordered or disordered. The effective
Ising action, determined via the lattice Schwinger-Dyson equations, contains
even (two-spin) and odd (one- and three-spin) terms with short range. We find
that the truncation to Ising degrees of freedom produces an effective action
which is discontinuous across the gauge theory's phase transition. This
discontinuity may disappear if the effective action is made more elaborate. | hep-lat |
Domain decomposition and multilevel integration for fermions: The numerical computation of many hadronic correlation functions is
exceedingly difficult due to the exponentially decreasing signal-to-noise ratio
with the distance between source and sink. Multilevel integration methods,
using independent updates of separate regions in space-time, are known to be
able to solve such problems but have so far been available only for pure gauge
theory. We present first steps into the direction of making such integration
schemes amenable to theories with fermions, by factorizing a given observable
via an approximated domain decomposition of the quark propagator. This allows
for multilevel integration of the (large) factorized contribution to the
observable, while its (small) correction can be computed in the standard way. | hep-lat |
THE QCD ABACUS: A New Formulation for Lattice Gauge Theories: A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from
color triplet Fermions --- the standard quarks and a new Fermionic
``constituent'' of the gluon we call ``rishons''. The quarks are represented by
Dirac spinors on each site and the gauge fields by rishon-antirishon bilinears
on each link which together with the local gauge transforms are the generators
of an SU(6) algebra. The effective Lagrangian for the path integral lives in
$R^4 \times S^1$ Euclidean space with a compact ``fifth time'' of circumference
($\beta$) and non-Abelian charge ($e^2$) both of which carry dimensions of
length. For large $\beta$, it is conjectured that continuum QCD is reached and
that the dimensionless ratio $g^2 = e^2/\beta$ becomes the QCD gauge coupling.
The quarks are introduced as Kaplan chiral Fermions at either end of the finite
slab in fifth time. This talk will emphasize the gauge and algebraic structure
of the rishon or link Fermions and the special properties that may lead to fast
discrete dynamics for numerical simulations and new theoretical insight. | hep-lat |
The principle of indirect elimination: The principle of indirect elimination states that an algorithm for solving
discretized differential equations can be used to identify its own
bad-converging modes. When the number of bad-converging modes of the algorithm
is not too large, the modes thus identified can be used to strongly improve the
convergence. The method presented here is applicable to any standard algorithm
like Conjugate Gradient, relaxation or multigrid. An example from theoretical
physics, the Dirac equation in the presence of almost-zero modes arising from
instantons, is studied. Using the principle, bad-converging modes are removed
efficiently. Applied locally, the principle is one of the main ingredients of
the Iteratively Smooting Unigrid algorithm. | hep-lat |
Fermion RG blocking transformations and IR structure: We explore fermion RG block-spinning transformations on the lattice with the
aim of studying the IR structure of gauge theories and, in particular, the
existence of IR fixed points for varying fermion content. In the case of light
fermions the main concern and difficulty is ensuring locality of any adopted
blocking scheme. We discuss the problem of constructing a local blocked fermion
action in the background of arbitrary gauge fields. We then discuss the
carrying out of accompanying gauge field blocking. In the presence of the
blocked fermions implementation of MCRG is not straightforward. By adopting
judicious approximations we arrive at an easily implementable approximate RG
recursion scheme that allows quick, inexpensive estimates of the location of
conformal windows for various groups and fermion representations. We apply this
scheme to locate the conformal windows in the case of SU(2) and SU(3) gauge
groups. Some of the reasons for the apparent efficacy of this and similar
decimation schemes are discussed. | hep-lat |
Onium Masses with Three Flavors of Dynamical Quarks: We have greatly extended an earlier calculation of the charmonium spectrum on
three flavor dynamical quark ensembles by using more recent ensembles generated
by the MILC collaboration. The heavy quarks are treated using the Fermilab
formulation. The charmonium state masses are in reasonable agreement with the
observed spectrum; however, some of the spin splittings may still be too small. | hep-lat |
The Euclidean two-point correlation function of the topological charge
density: We study the Euclidean two-point correlation function $G_q(x)$ of the
topological charge density in QCD. A general statement based on reflection
positivity tells us that $G_q(x)<0$ for $x\neq 0 $. On the other hand the
topological susceptibility $\chi_q=\int d^d x G_q(x)$ is a positive quantity.
This indicates that $G_q(x)$ developes a positive contact term at $x=0$, that
contributes to the determination of the physical value of $\chi_q$. We show
explicitly these features of $G_q(x)$ in a solvable nontrivial continuum model,
the two-dimensional $CP^{N-1}$ model in the large-N limit. A similar analysis
is done on the lattice. | hep-lat |
Performance of lattice QCD programs on CP-PACS: The CP-PACS is a massively parallel MIMD computer with the theoretical peak
speed of 614 GFLOPS which has been developed for computational physics
applications at the University of Tsukuba, Japan. We report on the performance
of the CP-PACS computer measured during recent production runs using our
Quantum Chromodynamics code for the simulation of quarks and gluons in particle
physics. With the full 2048 processing nodes, our code shows a sustained speed
of 237.5 GFLOPS for the heat-bath update of gluon variables, 264.6 GFLOPS for
the over-relaxation update, and 325.3 GFLOPS for quark matrix inversion with an
even-odd preconditioned minimal residual algorithm. | hep-lat |
Infrared behavior of the Faddeev-Popov operator in Coulomb gauge QCD: We calculate the eigenvalue distribution of the Faddeev-Popov operator in
Coulomb gauge QCD using quenched SU(3) lattice simulation. In the confinement
phase, the density of the low-lying eigenvalues increases with lattice volume,
and the confinement criterion is satisfied. Moreover, even in the deconfinement
phase, the behavior of the FP eigenvalue density is qualitatively the same as
in the confinement phase. This is consistent with the fact that the
color-Coulomb potential is not screened in the deconfined phase. | hep-lat |
Understanding Parton Distributions from Lattice QCD: Present Limitations
and Future Promise: This talk will explain how ground state matrix elements specifying moments of
quark density and spin distributions in the nucleon have been calculated in
full QCD, show how physical extrapolation to the chiral limit including the
physics of the pion cloud resolves previous apparent conflicts with experiment,
and describe the computational resources required for a definitive comparison
with experiment. | hep-lat |
(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver: We present a multigrid based eigensolver for computing low-modes of the
Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods
have already replaced conventional Krylov subspace solvers in many lattice QCD
computations. Since the $\gamma_5$-preserving aggregation based interpolation
used in our multigrid method is valid for both, the Hermitian and the
non-Hermitian case, inversions of very ill-conditioned shifted systems with the
Hermitian operator become feasible. This enables the use of multigrid within
shift-and-invert type eigensolvers. We show numerical results from our MPI-C
implementation of a Rayleigh quotient iteration with multigrid. For
state-of-the-art lattice sizes and moderate numbers of desired low-modes we
achieve speed-ups of an order of magnitude and more over PARPACK. We show
results and develop strategies how to make use of our eigensolver for
calculating disconnected contributions to hadronic quantities that are noisy
and still computationally challenging. Here, we explore the possible benefits,
using our eigensolver for low-mode averaging and related methods with high and
low accuracy eigenvectors. We develop a low-mode averaging type method using
only a few of the smallest eigenvectors with low accuracy. This allows us to
avoid expensive exact eigensolves, still benefitting from reduced statistical
errors. | hep-lat |
Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in
finite-volume: Whether one is interested in accessing the excited spectrum of hadrons or
testing the standard model of particle physics, electroweak transition
processes involving multi-hadron channels in the final state play an important
role in a variety of experiments. Presently the primary theoretical tool with
which one can study such reactions is lattice QCD, which is defined in a finite
spacetime volume. In this work, we investigate the feasibility of implementing
existing finite-volume formalism in realistic lattice QCD calculation of
reactions in which a stable hadron can transition to one of several two-hadron
channels under the action of an external current. We provide a conceptual
description of the coupled-channel transition formalism, a practical roadmap
for carrying out a calculation, and an illustration of the approach using
synthetic data for two non-trivial resonant toy models. The results provide a
proof-of-principle that such reactions can indeed be constrained using
modern-day lattice QCD calculations, motivating explicit computation in the
near future. | hep-lat |
First experiences with HMC for dynamical overlap fermions: We describe an HMC algorithm for dynamical overlap fermions which makes use
of their good chiral properties. We test the algorithm in the Schwinger model.
Topological sectors are readily changed even in the massless case. | hep-lat |
Fixed-scale approach to finite-temperature lattice QCD with shifted
boundaries: We study the thermodynamics of the SU(3) gauge theory using the fixed-scale
approach with shifted boundary conditions. The fixed-scale approach can reduce
the numerical cost of the zero-temperature part in the equation of state
calculations, while the number of possible temperatures is limited by the
integer $N_t$, which represents the temporal lattice extent. The shifted
boundary conditions can overcome such a limitation while retaining the
advantages of the fixed-scale approach. Therefore, our approach enables the
investigation of not only the equation of state in detail, but also the
calculation of the critical temperature with increased precision even with the
fixed-scale approach. We also confirm numerically that the boundary conditions
suppress the lattice artifact of the equation of state, which has been
confirmed in the non-interacting limit. | hep-lat |
Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical
Staggered Fermions: Complete spectra of the staggered Dirac operator $\Dirac$ are determined in
quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of
dynamical fermions.
Periodic as well as antiperiodic boundary conditions are used.
An attempt is made to relate the performance of multigrid (MG) and conjugate
gradient (CG) algorithms for propagators with the distribution of the
eigenvalues of~$\Dirac$.
The convergence of the CG algorithm is determined only by the condition
number~$\kappa$ and by the lattice size.
Since~$\kappa$'s do not vary significantly when quarks become dynamic,
CG convergence in unquenched fields can be predicted from quenched
simulations.
On the other hand, MG convergence is not affected by~$\kappa$ but depends on
the spectrum in a more subtle way. | hep-lat |
Radiative improvement of the lattice NRQCD action using the background
field method and application to the hyperfine splitting of quarkonium states: We present the first application of the background field method to
Non-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop
radiative corrections to the coefficients of the NRQCD action in a manifestly
gauge-covariant manner. The coefficient of the $\sigma\cdot B$ term in the
NRQCD action is computed at the one-loop level; the resulting shift of the
hyperfine splitting of bottomonium is found to bring the lattice predictions in
line with experiment. | hep-lat |
Light quark correlators in a mixed-action setup: We report our progress in simulating Neuberger valence fermions on N_f=2
Wilson O(a)-improved sea quarks. We compute correlators with valence quark
masses both in the p- and in the epsilon-regime, and we match the results with
the predictions of the Chiral Effective Theory in the mixed regime. This allows
us to extract the Low Energy Couplings (LECs) of the N_f=2 theory and to test
the validity of the approach. | hep-lat |
Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High
Temperature Phase of QCD: We investigate the low-lying eigenmodes of the Dirac matrix with the aim to
gain more insight into the temperature dependence of the anomalous $U_A(1)$
symmetry. We use the overlap operator to probe dynamical QCD configurations
generated with (2+1)-flavors of highly improved staggered quarks. We find no
evidence of a gap opening up in the infrared region of the eigenvalue spectrum
even at $1.5\,T_c$, $T_c$ being the chiral crossover temperature. Instead, we
observe an accumulation of near-zero eigenmodes. We argue that these near-zero
eigenmodes are primarily responsible for the anomalous breaking of the axial
symmetry still being effective. At $1.5\,T_c$, these near-zero eigenmodes
remain localized and their distribution is consistent with the dilute instanton
gas picture. At this temperature, the average size of the instantons is
$0.223(8)\,\text{fm}$ and their density is $0.147(7)\,\text{fm}^{-4}$. | hep-lat |
The Coulomb flux tube revisited: We perform $SU(2)$ Yang-Mills lattice simulation of the electric field
distribution in the Coulomb gauge for different values of $\beta$ to further
investigate the nature of the Coulomb flux tube. | hep-lat |
Critical Behavior of the Schwinger Model with Wilson Fermions: We present a detailed analysis, in the framework of the MFA approach, of the
critical behaviour of the lattice Schwinger model with Wilson fermions on
lattices up to $24^2$, through the study of the Lee-Yang zeros and the specific
heat. We find compelling evidence for a critical line ending at $\kappa = 0.25$
at large $\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2,
20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation
is verified in the explored $\beta$ region. | hep-lat |
Lattice study of the Schwinger model at fixed topology: At small lattice spacing QCD simulations are expected to become stuck in a
single topological sector. Observables evaluated in a fixed topological sector
differ from their counterparts in full QCD, i.e. at unfixed topology, by volume
dependent corrections. We investigate these corrections in the two-flavor
Schwinger model, which is in several aspects similar to QCD, using Wilson
fermions. We also try to remove these corrections by suitable extrapolations to
infinite volume. | hep-lat |
The static energy of a quark-antiquark pair from Laplacian eigenmodes: We test a method for computing the static quark-antiquark potential in
lattice QCD, which is not based on Wilson loops, but where the trial states are
formed by eigenvector components of the covariant lattice Laplace operator. The
runtime of this method is significantly smaller than the standard Wilson loop
calculation, when computing the static potential not only for on-axis, but also
for many off-axis quark-antiquark separations, i.e., when a fine spatial
resolution is required. We further improve the signal by using multiple
eigenvector pairs, weighted with Gaussian profile functions of the eigenvalues,
providing a basis for a generalized eigenvalue problem (GEVP), as it was
recently introduced to improve distillation in meson spectroscopy. We show
results with the new method for the static potential with dynamical fermions
and demonstrate its efficiency compared to traditional Wilson loop
calculations. The method presented here can also be applied to compute hybrid
or tetra-quark potentials and to static-light systems. | hep-lat |
Fisher's zeros as boundary of RG flows in complex coupling space: We discuss the possibility of extending the RG flows to complex coupling
spaces. We argue that the Fisher's zeros are located at the boundary of the
complex basin of attraction of IR fixed points. We support this picture with
numerical calculations at finite volume for2D O(N) models in the large-N limit
and the hierarchical Ising model using the two-lattice matching method. We
present numerical evidence supporting the idea that, as the volume increases,
the Fisher's zeros of 4-dimensional pure gauge SU(2) lattice gauge theory with
a Wilson action, stabilize at a distance larger than 0.1 from the real axis in
the complex beta=4/g^2 plane. We show that when a positive adjoint term is
added, the zeros get closer to the real axis. We compare the situation with the
U(1) case. We discuss the implications of this new framework for proofs of
confinement and searches for nontrivial IR fixed points in models beyond the
standard model. | hep-lat |
A study of center and chiral symmetry realization in thermal
$\mathcal{N}=1$ super Yang-Mills theory using the gradient flow: The realization of center and chiral symmetries in $\mathcal{N}=1$ super
Yang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice
by means of Monte Carlo methods. At zero temperature this theory is expected to
confine external fundamental charges and to have a non-vanishing gaugino
condensate, which breaks the non-anomalous Z$_{2\textrm{N}_{c}}$ chiral
symmetry. In previous studies at finite temperatures, the phase transitions
corresponding to deconfinement and chiral restoration were observed to occur at
roughly the same critical temperature for SU(2) gauge group. We find further
evidences for this observation from new measurements at smaller lattice
spacings using the fermion gradient flow, and we discuss the agreement of our
findings with conjectures from superstring theory. The implementation of the
gradient flow technique allows us also to estimate, for the first time, the
condensate at zero temperatures and zero gaugino mass with Wilson fermions. | hep-lat |
Lattice QCD calculation of the electroweak box diagrams for the kaon
semileptonic decays: We present a lattice QCD calculation of the axial $\gamma W$-box diagrams
relevant for the kaon semileptonic decays. We utilize a recently proposed
method, which connects the electroweak radiative corrections in Sirlin's
representation to that in chiral perturbation theory. It allows us to use the
axial $\gamma W$-box correction in the SU(3) limit to obtain the low energy
constants for chiral perturbation theory. From first principles our results
confirm the previously used low energy constants provided by the minimal
resonance model with a significant reduction in uncertainties. | hep-lat |
Leading order mesonic and baryonic SU(3) low energy constants from $N_f
= 3$ lattice QCD: We determine the leading order mesonic~($B_0$ and $F_0$) and baryonic~($m_0$,
$D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice
QCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$)
non-perturbatively improved Wilson fermions at six distinct values of the
lattice spacing in the range $a\approx (0.039 - 0.098)$ fm, which constitute a
subset of the Coordinated Lattice Simulations (CLS) gauge ensembles. The
pseudoscalar meson mass $M_\pi$ ranges from around $430$ MeV down to $240$ MeV
and the linear spatial lattice extent $L$ from $6.4\,M_{\pi}^{-1}$ to
$3.3\,M_{\pi}^{-1}$, where $ L M_\pi \geq 4$ for the majority of the ensembles.
This allows us to perform a controlled extrapolation of all the low energy
constants to the chiral, infinite volume and continuum limits. We find the
SU(3) chiral condensate and $F_0$ to be smaller than their SU(2) counterparts
while the Gell-Mann--Oakes--Renner parameters $B_0\approx B$ are similar.
Regarding baryonic LECs, we obtain $F/D = 0.612^{(14)}_{(12)}$. | hep-lat |
Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge
Theories: We construct canonical transformations to reformulate SU(N) Kogut-Susskind
lattice gauge theory in terms of a set of fundamental loop & string flux
operators along with their canonically conjugate loop & string electric fields.
We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of
freedom become cyclic and decouple from the physical Hilbert space ${\cal
H}^p$. The canonical relations between the initial SU(N) link operators and the
final SU(N) loop & string operators over the entire lattice are worked out in a
self consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of
the fundamental physical loop operators has global SU(N) invariance. There are
no gauge fields. We further show that the $(1/g^2)$ magnetic field terms on
plaquettes create and annihilate the fundamental plaquette loop fluxes while
the $(g^2)$ electric field terms describe all their interactions. In the weak
coupling ($g^2 \rightarrow 0$) continuum limit the SU(N) loop dynamics is
described by SU(N) spin Hamiltonian with nearest neighbour interactions. In the
simplest SU(2) case, where the canonical transformations map the SU(2) loop
Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special
role of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loop
dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge
invariant hydrogen atom loop basis is discussed. | hep-lat |
Improved actions and lattice coarsening effects in MCRG studies in SU(2)
LGT: We study decimation procedures and effective (improved) actions in the
framework of Monte Carlo Renormalization Group (MCRG). Particular attention is
paid to matching the form of the effective action to the decimation procedure
parameters. Using the static quark-antiquark potential in SU(2) LGT we probe
different distance scales and find that an effective action containing multiple
group representations is capable of reproducing long distance physics well. In
particular, appropriate matching results in the practical elimination of the
coarsening/fining effect of the lattice spacing under decimation. The short
distance regime of the effective theory is also studied. We next carry out
studies of effective actions involving both multiple representations and loops
beyond the single plaquette towards determining an improved action good over a
wide length scale regime. | hep-lat |
Nucleon form factors and root-mean-square radii on a (10.8 fm$)^4$
lattice at the physical point: We present the nucleon form factors and root-mean-square (RMS) radii measured
on a (10.8 fm$)^4$ lattice at the physical point. We compute the form factors
at small momentum transfer region in $q^2\le 0.102$ GeV$^2$ with the standard
plateau method choosing four source-sink separation times $t_{\rm sep}$ from
0.84 to 1.35 fm to examine the possible excited state contamination. We obtain
the electric and magnetic form factors and their RMS radii for not only the
isovector channel but also the proton and neutron ones without the disconnected
diagram. We also obtain the axial-vector coupling and the axial radius from the
axial-vector form factor. We find that these three form factors do not show
large $t_{\rm sep}$ dependence in our lattice setup. On the other hand, the
induced pseudoscalar and pseudoscalar form factors show the clear effects of
the excited state contamination, which affect the generalized
Goldberger-Treiman relation. | hep-lat |
Derivation of Chiral Lagrangians from Random Lattice QCD: In our work we extend the ideas of the derivation of the chiral effective
theory from the lattice QCD [1] to the case of the random lattice
regularization of QCD. Such procedure allows in principle to find contribution
of any order into the chiral effective lagrangian. It is shown that an infinite
subseries of the chiral perturbation can be summed up into tne Born-Infeld term
and the logarithmic correction to them. | hep-lat |
Supersymmetric Yang-Mills Theories from Domain Wall Fermions: We present work in progress on employing domain wall fermions to simulate N=1
supersymmetric Yang-Mills theories on the lattice in d=4 and d=3 dimensions.
The geometrical nature of domain wall fermions gives simple insights into how
to construct these theories. We also discuss the obstacles associated with
simulating the N=2 theory in d=4. | hep-lat |
Ginsparg-Wilson relation and lattice Weyl fermions: We demonstrate that in the topologically trivial gauge sector the
Ginsparg-Wilson relation for lattice Dirac operators admits an exactly gauge
invariant path integral formulation of the Weyl fermions on a lattice. | hep-lat |
Probing the Region of Massless Quarks in Quenched Lattice QCD using
Wilson Fermions: We study the spectrum of $H(m)=\gamma_5 W(-m)$ with $W(m)$ being the
Wilson-Dirac operator on the lattice with bare mass equal to $m$. The
background gauge fields are generated using the SU(3) Wilson action at
$\beta=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of
$H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is
massless in this whole region. | hep-lat |
Comment on "The QCD axion beyond the classical level: A lattice study": We rebut the claim by Nakamura and Schierholz [1] that the mass of a
potential axion needs to be no less than ~230MeV pointing out errors in both
their analytic argument and numerical simulations. | hep-lat |
Gluon gravitational structure of hadrons of different spin: The gravitational form factors (GFFs) of hadrons encode the matrix elements
of the energy momentum tensor of QCD. These quantities describe how energy,
spin, and various mechanical properties of hadrons are carried by their quark
and gluon constituents. We present the gluon GFFs of the pion, nucleon, $\rho$
meson, and $\Delta$ baryon as functions of the squared momentum transfer $t$ in
the region $0 \leq -t < 2 \; \text{GeV}^2$, as determined in a lattice QCD
study with pion mass $m_{\pi} = 450(5) \; \text{MeV}$. By fitting the extracted
GFFs using multipole and z-parameter expansion functional forms, we extract
various gluon contributions to the energy, pressure, and shear force
distributions of the hadrons in the 3D and 2D Breit frames as well as in the
infinite momentum frame. We also obtain estimates for the corresponding gluon
mechanical and mass radii, as well as the forward-limit gluon contributions to
the momentum fraction and angular momentum of the hadrons. | hep-lat |
Spontaneous supersymmetry breaking in the two-dimensional N=1
Wess-Zumino model: We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on
the lattice using Wilson fermions and the fermion loop formulation. We give a
complete nonperturbative determination of the ground state structure in the
continuum and infinite volume limit. We also present a determination of the
particle spectrum in the supersymmetric phase, in the supersymmetry broken
phase and across the supersymmetry breaking phase transition. In the
supersymmetry broken phase we observe the emergence of the Goldstino particle. | hep-lat |
B Meson Decay Constants Using NRQCD: Recent results for B meson decay constants with NRQCD b-quarks and clover
light quarks are discussed. Perturbative matching factors through O($\alpha/M$)
are now available and incorporated into the analyses. An O($\alpha a$)
improvement term to the heavy-light axial current is identified and included.
The slope of $f_{PS}\sqrt{M_{PS}}$ versus $1/M_{PS}$ is significantly reduced
by these corrections. | hep-lat |
Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion
Electromagnetic Form Factor: We investigate the utility of partially twisted boundary conditions in
lattice calculations of meson observables. For dynamical simulations, we show
that the pion dispersion relation is modified by volume effects. In the isospin
limit, we demonstrate that the pion electromagnetic form factor can be computed
on the lattice at continuous values of the momentum transfer. Furthermore, the
finite volume effects are under theoretical control for extraction of the pion
charge radius. | hep-lat |
Topological susceptibility of $2d~\mathrm{CP}^1$ or $\mathrm{O}(3)$
non-linear $σ$-model: is it divergent or not?: The topological susceptibility of $2d$ $\mathrm{CP}^{N-1}$ models is
expected, based on perturbative computations, to develop a divergence in the
limit $N \to 2$, where these models reduce to the well-known non-linear
$\mathrm{O}(3)$ $\sigma$-model. The divergence is due to the dominance of
instantons of arbitrarily small size and its detection by numerical lattice
simulations is notoriously difficult, because it is logarithmic in the lattice
spacing. We approach the problem from a different perspective, studying the
behavior of the model when the volume is fixed in dimensionless lattice units,
where perturbative predictions are turned into more easily checkable behaviors.
After testing this strategy for $N = 3$ and $4$, we apply it to $N = 2$,
adopting at the same time a multicanonic algorithm to overcome the problem of
rare topological fluctuations on asymptotically small lattices. Our final
results fully confirm, by means of purely non-perturbative methods, the
divergence of the topological susceptibility of the $2d$ $\mathrm{CP}^1$ model. | hep-lat |
Monopole Loop Distribution and Confinement in SU(2) Lattice Gauge Theory: The abelian-projected monopole loop distribution is extracted from maximal
abelian gauge simulations. The number of loops of a given length falls as a
power of the length nearly independent of lattice size. This power increases
with $\beta=4/g^2$, reaching five around $\beta=2.85$, beyond which loops any
finite fraction of the lattice size vanish in the infinite lattice limit,
suggesting the continuum theory lacks confinement. | hep-lat |
Weak Coupling Limit of U(1) Lattice Model in Fourier Basis: The transfer-matrix of the U(1) lattice model is considered in the Fourier
basis and in the weak coupling limit. The issues of Gauss law constraint and
gauge invariant states are addressed in the Fourier basis. In particular, it is
shown that in the strong coupling limit the gauge invariant Fourier states are
effectively the finite size closed loop currents. In the weak coupling limit,
however, the link-currents along periodic or infinite spatial directions find
comparable roles as gauge invariant states. The subtleties related to the
extreme weak coupling of the transfer-matrix in the Fourier basis are
discussed. A careful analysis of the zero eigenvalues of the matrix in the
quadratic action leads to a safe extraction of the diverging group volume in
the limit $g\to 0$. By means of the very basic notions and tools of the lattice
model, the spectrum at the weak coupling limit for any dimension and size of
lattice is obtained analytically. The spectrum at the weak coupling limit
corresponds to the expected one by the continuum model in the large lattice
limit. | hep-lat |
Running coupling in SU(2) with adjoint fermions: We present a measurement of the Schr\"odinger Functional running coupling in
SU(2) lattice gauge theory with adjoint fermions. We use HEX smearing and
clover improvement to reduce the discretization effects. We obtain a robust
continuum limit for the step scaling, which confirms the existence of a
non-trivial fixed point. | hep-lat |
Spectral Analysis of Causal Dynamical Triangulations via Finite Element
Method: We examine the dual graph representation of simplicial manifolds in Causal
Dynamical Triangulations (CDT) as a mean to build observables, and propose a
new representation based on the Finite Element Methods (FEM). In particular,
with the application of FEM techniques, we extract the (low-lying) spectrum of
the Laplace-Beltrami (LB) operator on the Sobolev space $H^1$ of scalar
functions on piecewise flat manifolds, and compare them with corresponding
results obtained by using the dual graph representation. We show that, besides
for non-pathological cases in two dimensions, the dual graph spectrum and
spectral dimension do not generally agree, neither quantitatively nor
qualitatively, with the ones obtained from the LB operator on the continuous
space. We analyze the reasons of this discrepancy and discuss its possible
implications on the definition of generic observables built from the dual graph
representation. | hep-lat |
The dependence of observables on action parameters: Many applications in Lattice field theory require to determine the Taylor
series of observables with respect to action parameters. A primary example is
the determination of electromagnetic corrections to hadronic processes. We show
two possible solutions to this general problem, one based on reweigting, that
can be considered a generalization of the RM123 method. The other based on the
ideas of Numerical Stochastic Perturbation Theory (NSPT) in the Hamiltonian
formulation. We show that 1) the NSPT-based approach shows a much reduced
variance in the determination of the Taylor coefficients, and 2) That both
approaches are related by a change of variables. Numerical results are shown
for the case of $\lambda-\phi^4$ in 4 dimensions, but we expect these
observations to be general. We conclude by commenting on the possible use of
Machine Learning techniques to find similar change of variables that can
potentially reduce the variance in Taylor coefficients. | hep-lat |
$ρ$ meson decay on asymmetrical lattices: We present a lattice QCD calculation of the characteristics of the $\rho$
meson decay. The study is carried out on spatially asymmetric boxes using
nHYP-smeared clover fermions in the quenched approximation. The resonance mass
and coupling constant are calculate using the P-wave scattering phaseshifts, of
the isospin I=1 two-pion system. We use pion masses m_{\pi}= 418 MeV and
m_{\pi}=312 MeV. In both cases, the $\rho$ decay is kinematically feasible. We
work on lattice sizes N_z X 24^2 X 48 with lattice spacing a=0.1 fm and
N_z=24,30,34,48. | hep-lat |
Dynamical quantum phase transitions in a noisy lattice gauge theory: Lattice gauge theories (LGTs) form an intriguing class of theories highly
relevant to both high-energy particle physics and low-energy condensed matter
physics with the rapid development of engineered quantum devices providing new
tools to study e.g. dynamics of such theories. The massive Schwinger model is
known to exhibit intricate properties of more complicated theories and has
recently been shown to undergo dynamical quantum phase transitions out of
equilibrium. With current technology, noise is inevitable and potentially fatal
for a successful quantum simulation. This paper studies the dynamics subject to
noise of a $(1+1)$D U$(1)$ quantum link model following a quench of the sign of
the mass term. We find that not only is the system capable of handling noise at
rates realistic in NISQ-era devices, promising the possiblity to study the
target dynamics with current technology, but the effect of noise can be
understood in terms of simple models. Specifically the gauge-breaking nature of
bit-flip channels results in exponential dampening of state amplitudes, and
thus observables, which does not affect the structures of interest. This is
especially important as it demonstrates that the gauge theory can be
successfully studied with devices that only exhibit approximate gauge
invariance. | hep-lat |
Dynamics of the 2d Potts model phase transition: The dynamics of 2d Potts models, which are temperature driven through the
phase transition using updating procedures in the Glauber universality class,
is investigated. We present calculations of the hysteresis for the (internal)
energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used
to define finite volume estimators of physical observables, which can be used
to study the approach to the infinite volume limit. We compare with equilibrium
configurations and the preliminary indications are that the dynamics leads to
considerable alterations of the statistical properties of the configurations
studied. | hep-lat |
Study of Chiral Symmetry and $U(1)_A$ using Spatial Correlators for
$N_f=2+1$ QCD at finite temperature with Domain Wall Fermions: Based on simulations of 2+1 flavor lattice QCD with M\"obius domain wall
fermions at high temperatures, we compute a series of spatial correlation
functions to study the screening masses in mesonic states. We compare these
masses with the symmetry relations for various quark masses and lattice sizes
at temperatures above the critical point. Using these spatial correlation
functions we examine the $SU(2)_L \times SU(2)_R$ symmetry as well as the
anomalously broken axial $U(1)_A$ symmetry. Additionally we explore a possible
and emergent chiral-spin symmetry $SU(2)_{CS}$. | hep-lat |
Decomposition of the static potential in SU(3) gluodynamics: After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we
decompose the nonabelian gauge field into the Abelian field created by Abelian
monopoles and the modified nonabelian field with monopoles removed. We then
calculate respective static potentials in the fundamental representation and
show that the sum of these potentials approximates the nonabelian static
potential with good precision at all distances considered. Comparison with
other ways of decomposition is made. | hep-lat |
Higher moments of charge fluctuations in QCD at high temperature: We present lattice results for baryon number, strangeness and electric charge
fluctuations as well as their correlations at finite temperature and vanishing
chemical potentials, i.e. under conditions relevant for RHIC and LHC. We find
that the fluctuations change rapidly at the transition temperature $T_c$ and
approach the ideal quark gas limit already at approximately $1.5T_c$. This
indicates that quarks are the relevant degrees of freedom that carry the
quantum numbers of conserved charges at $T\geq 1.5T_c$. At low temperature,
qualitative features of the lattice results are well described by a hadron
resonance gas model. | hep-lat |
SU(2) Flux Distributions on Finite Lattices: We studied SU(2) flux distributions on four dimensional euclidean lattices
with one dimension very large. By choosing the time direction appropriately we
can study physics in two cases: one is finite volume in the zero temperature
limit, another is finite temperature in the the intermediate to large volume
limit. We found that for cases of beta > beta crit there is no intrinsic string
formation. Our lattices with beta > beta crit belong to intermediate volume
region, and the string tension in this region is due to finite volume effects.
In large volumes we found evidence for intrinsic string formation. | hep-lat |
2018 Update on $\varepsilon_K$ with lattice QCD inputs: We present updated results for $\varepsilon_K$ determined directly from the
standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$,
$|V_{us}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $F_K$, and $m_c$. We find that
the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs
describes only 70% of the experimental value of $|\varepsilon_K|$ and does not
explain its remaining 30%, which leads to a strong tension in $|\varepsilon_K|$
at the $4\sigma$ level between the SM theory and experiment. We also find that
this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained
using the heavy quark expansion based on QCD sum rules. | hep-lat |
Polarized and Unpolarized Nucleon Structure Functions from Lattice QCD: We report on a high statistics quenched lattice QCD calculation of the
deep-inelastic structure functions $F_1$, $F_2$, $g_1$ and $g_2$ of the proton
and neutron. The theoretical basis for the calculation is the operator product
expansion. We consider the moments of the leading twist operators up to spin
four. Using Wilson fermions the calculation is done for three values of
$\kappa$, and we perform the extrapolation to the chiral limit. The
renormalization constants, which lead us from lattice to continuum operators,
are calculated in perturbation theory to one loop order. | hep-lat |
Negative moment of inertia and rotational instability of gluon plasma: Using first-principle numerical simulations of the lattice SU(3) gauge
theory, we calculate the isothermal moment of inertia of the rigidly rotating
gluon plasma. We find that the moment of inertia unexpectedly takes a negative
value below the "supervortical temperature" $T_s = 1.50(10) T_c$, vanishes at
$T = T_s$, and becomes a positive quantity at higher temperatures. The negative
moment of inertia indicates a thermodynamic instability of rigid rotation. We
derive the condition of thermodynamic stability of the vortical plasma and show
how it relates to the scale anomaly and the magnetic gluon condensate. The
rotational instability of gluon plasma shares a striking similarity with the
rotational instabilities of spinning Kerr and Myers-Perry black holes. | hep-lat |
Coulomb gauge studies of SU(3) Yang-Mills theory on the lattice: We study the infrared behaviour of lattice SU(3) Yang-Mills theory in Coulomb
gauge in terms of the ghost propagator, the Coulomb potential and the
transversal and the time-time component of the equal-time gluon propagator. In
particular, we focus on the Gribov problem and its impact on the observables.
We observe that the simulated annealing method is advantageous for fixing the
Coulomb gauge in large volumes. We study finite size and discretization
effects. While finite size effects can be controlled by the cone cut, and the
ghost propagator and the Coulomb potential become scaling functions with the
cylinder cut, the equal-time gluon propagator does not show scaling in the
considered range of the inverse coupling constant. The ghost propagator is
infrared enhanced. The Coulomb potential is now extended to considerably lower
momenta and shows a more complicated infrared regime. The Coulomb string
tension satisfies Zwanziger's inequality, but its estimate can be considered
only preliminary because of the systematic Gribov effect that is particularly
strong for the Coulomb potential. | hep-lat |
Making chiral fermion actions (almost) gauge invariant using Laplacian
gauge fixing: Straight foreward lattice descriptions of chiral fermions lead to actions
that break gauge invariance. I describe a method to make such actions gauge
invariant (up to global gauge transformations) with the aid of gauge fixing. To
make this prescription unambiguous, Laplacian gauge fixing is used, which is
free from Gribov ambiguities. | hep-lat |
Continuum Results for Light Hadronic Quantities using Domain Wall
Fermions with the Iwasaki and DSDR Gauge Actions: We present preliminary continuum results for light hadronic quantities
obtained by the RBC/UKQCD collaboration using domain wall fermions with both
the Iwasaki and the novel Dislocation Suppressing Determinant Ratio (DSDR)
gauge actions. The DSDR action allows us to simulate at near physical quark
masses on a larger, coarser lattice (a^-1 = 1.4 GeV, L = 4.6 fm) while
retaining good chiral symmetry properties. We discuss our ongoing combined
analysis of the three ensemble sets and give early results for the pion and
kaon decay constants, quark masses and B_K. | hep-lat |
Solitons and spontaneous symmetry breaking in 2 and 4 dimensions: We show that mass generation in 1+1 and 3+1 dimensions may occur together
with spontaneous symmetry breaking. | hep-lat |
Aspects of Chiral Symmetry and the Lattice: I explore the non-perturbative issues entwining lattice gauge theory,
anomalies, and chiral symmetry. After briefly reviewing the importance of
chiral symmetry in particle physics, I discuss how anomalies complicate lattice
formulations. Considerable information can be deduced from effective chiral
Lagrangians, helping interpret the expectations for lattice models and
elucidating the role of the CP violating parameter $\Theta$. I then turn to a
particularly elegant scheme for exploring this physics on the lattice. This
uses an auxiliary extra space-time dimension, with the physical world being a
four dimensional interface. | hep-lat |
The Polyakov Loop and the Eigenvalues of the Dirac Operator: Aiming at the link between confinement and chiral symmetry the Polyakov loop
represented as a spectral sum of eigenvalues of the Dirac operator was subject
of recent studies. We analyze the volume dependence as well as the continuum
behavior of this quantity for quenched QCD using staggered fermions.
Furthermore, we present first results using dynamical configurations. | hep-lat |
Expressing the three-particle finite-volume spectrum in terms of the
three-to-three scattering amplitude: In this article we complete our formalism relating the finite-volume energy
spectrum of a scalar quantum field theory to the three-to-three scattering
amplitude, ${\cal M}_3$. In previous work we found a quantization condition
relating the spectrum to a non-standard infinite-volume quantity, denoted
${\cal K}_{{\rm df},3}$. Here we present the relation between ${\cal K}_{{\rm
df},3}$ and ${\cal M}_3$. We then discuss briefly how our now completed
formalism can be practically implemented to extract ${\cal M}_3$ from the
finite-volume energy spectrum. | hep-lat |
$B\to D^{(\ast)}\ellν$ at non-zero recoil: $B$ anomalies play a prominent role in Beyond the Standard Model (BSM)
physics searches. In particular, the long standing tension between the
inclusive and the exclusive determinations of the CKM matrix element $|V_{cb}|$
and the current tensions in the $R(D)$--$R(D^\ast)$ plane between theory and
experiment have brought the $B\to D^{(\ast)}\ell\nu$ semileptonic processes to
the spotlight. Existing lattice-QCD calculations of the $B\to D\ell\nu$ form
factors at non-zero recoil are being complemented with very recent developments
in the $B\to D^\ast\ell\nu$ channel. In this review I discuss recent progress
in lattice calculations of $B\to D^{(\ast)}\ell\nu$, as well as the
implications of these results for high precision determinations of $|V_{cb}|$
and the Lepton Flavor Universality (LFU) ratios $R(D^{(\ast)})$. | hep-lat |
Lattice QCD at non-zero baryon number: We discuss the quenched limit of lattice QCD at non-zero baryon number
density. We find evidence for a mixed phase that becomes broader with
increasing baryon number. Although the action is explicitly Z(3) symmetric the
Polyakov loop expectation value becomes non-zero already in the low temperature
phase. It indicates that the heavy quark potential stays finite at large
distances, i.e. the string between static quarks breaks at non-zero baryon
number density already in the hadronic phase. This behaviour is validated by
calculating the heavy quark potential using Polyakov loop correlations. | hep-lat |
Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model
Embedding: We investigate SU(2) gauge fields topology using new approach, which exploits
the well known connection between SU(2) gauge theory and quaternionic
projective sigma-models and allows to formulate the topological charge density
entirely in terms of sigma-model fields. The method is studied in details and
for thermalized vacuum configurations is shown to be compatible with
overlap-based definition. We confirm that the topological charge is distributed
in localized four dimensional regions which, however, are not compatible with
instantons. Topological density bulk distribution is investigated at different
lattice spacings and is shown to possess some universal properties. | hep-lat |
On the fractal structure of two-dimensional quantum gravity: We provide evidence that the Hausdorff dimension is 4 and the spectral
dimension is 2 for two-dimensional quantum gravity coupled the matter with a
central charge $c \leq 1$. For $c > 1$ the Hausdorff dimension and the spectral
dimension monotonously decreases to 2 and 1, respectively. | hep-lat |
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